RE: [Axiom-math] Engineering Application

[Herb Martin]

From: Bill Page
> On January 22, 2006 8:00 PM Raymond E. Rogers wrote:
> > Assuming I get axiom running; would anybody be willing to discuss
> > an engineering application where I think Algebraic Geometry provides
> > a mathematically correct answer? Even though I have just started
> > learning AG, I think I can do all of the hard work myself.
> 
> I would be very happy to discuss engineering applications of
> algebraic geometry.
> 
> Perhaps one place to start with Axiom and algebraic geometry might be
> the following tutorial by Donu Arapura 
> (http://www.math.purdue.edu/~dvb):
> 
> http://www.math.purdue.edu/~dvb/algeom.html
> 
> Introduction to Algebraic Geometry
> 
> Arapura includes some computer examples using Maple. We could see how
> we might do the same examples using Axiom.

I too am (newly) interested in Algebraic Geometry
and would prefer to pursue that in Axiom or another
free CAS (rather than Maple) since this is only a
hobby interest for me.

>From the links you (so kindly) offered I also found
the following:

Macaulay2 Home Page http://www.math.uiuc.edu/Macaulay2/
  A software system devoted to supporting research
  in algebraic geometry and commutative algebra.
  
Computations in algebraic geometry with Macaulay 2, 
 edited by David Eisenbud, Daniel R. Grayson, Michael
 E. Stillman, and Bernd Sturmfels.  Springer-Verlag
 September 25, ISBN 3-540-42230-7, $44.95. 
 http://www.math.uiuc.edu/Macaulay2/Book/  (FREE DOWNLOAD)

In no way am I trying to move the discussion away
from Axiom, but I am interest in the subjects no
matter what the tools (if the price is right.)
 
And these links seem related, depending on the
relationship with Algebraic Topology and if Geometric
Algebra has the same meaning (do they relate?)

Algebraic Topology
  Homotopy & homology spaces are discussed beginning 
  in Chapter 0 (Geometric introduction)
  http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Clifford's Geometric Algebra of Physical Space (APS). 
  http://www.uwindsor.ca/users/b/baylis/main.nsf
  The intention is to explain the use of paravectors 
  in the algebra to model spacetime.
 Relativity in Introductory Physics
 http://arxiv.org/abs/physics/0406158 
 Also available: GAWorkBook

Disclosure:  I am directly trying to gain a (much) 
better appreciation and understanding of the 
"The Road to Reality: A Complete Guide to the Laws 
of the Universe" by Roger Penrose.
 
--
Herb Martin